Design of piezoelectric microtransducers based on the topology optimization method

In this work, a systematic procedure based on the topology optimization method to design piezoelectric transducers in a static in-plane and out-of-plane framework is presented. The layout of the host structure and the electrode profile of the piezoelectric material are optimized simultaneously. Our numerical approach shows a significant improvement by using simultaneous optimization rather than optimizing separately the host structure and the electrode profile. Two important issues in this problem are the appearance of large gray areas (a mixture of solid and void material) in the optimized designs for the in-plane case and branches (disconnected areas) for the out-of-plane one, that actually distort the real performance of such transducers. To solve these problems and in order to obtain efficient and really close to 0-1 designs, a new interpolation function, appearing in the objective function for the sensor and in the source term for the actuator, is required. Thanks to the reciprocity of the piezoelectric effect, we get to prove analytically and to corroborate numerically how such a fact leads to the same optimized designs for sensors and actuators. A similar approach has shown quite good performance in the design of modal sensors/actuators, although restricted to the design of the electrode layout for a given structure. Finally, some of the optimized designs for the in-plane case have been fabricated. In several cases passive pieces are included to study movement into fluids.